Strongly correlated excitons in moiré semiconductors

Abstract

Moiré transition metal dichalcogenide (TMD) bilayers have emerged as a versatile platform for exploring a wide range of correlated electronic phenomena. In optical studies of these semiconducting systems, excitons—bound electron-hole pairs—play a crucial role by linking electronic correlations to optical responses. This thesis develops theoretical frameworks to understand how excitonic behavior interplays with various correlated states in moiré TMD bilayers and the resulting implications for optical measurements.

We begin by investigating the interaction between a single moiré exciton and Wigner crystal states formed by doped electrons. Focusing on systems with repulsive electron–exciton interactions, we discuss a scenario where excitons move within the complementary lattice of the charge-ordered electrons. As different Wigner crystal configurations emerge at specific electron filling fractions, the effective exciton lattice changes accordingly, giving rise to distinct spectral and topological features. These characteristics can serve as optical signatures of the underlying charge order, and we propose a momentum- and polarization-resolved reflection experiment to detect them.

Next, we turn to undoped bilayers hosting multiple moiré excitons. While prior work often models these systems using a Bose-Hubbard framework, we show that their commutation relations deviate from those of conventional bosons. Instead, the excitons obey algebra similar to that of angular momentum operators, resulting in a finite Hilbert space and limiting local exciton occupancy to two or three, depending on the bilayer's specific parameters. We demonstrate that this occupancy constraint could manifest in high-intensity optical pumping experiments.

Finally, we explore exciton dynamics in a doped heterobilayer where the topmost valence moiré band forms an antiferromagnetic Mott insulator. We present a theoretical model describing the coupling between the exciton and the spin background, revealing that spin fluctuations substantially narrow the exciton’s effective bandwidth—by orders of magnitude compared to its non-interacting counterpart. This suppression in mobility provides a measurable contrast, which we suggest can be probed through exciton diffusion experiments.